Problem: The following line passes through point $(-1, 1)$ : $y = \dfrac{5}{9} x + b$ What is the value of the $y$ -intercept $b$ ?
Substituting $(-1, 1)$ into the equation gives: $1 = \dfrac{5}{9} \cdot -1 + b$ $1 = -\dfrac{5}{9} + b$ $b = 1 + \dfrac{5}{9}$ $b = \dfrac{14}{9}$ Plugging in $\dfrac{14}{9}$ for $b$, we get $y = \dfrac{5}{9} x + \dfrac{14}{9}$. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ $(-1, 1)$